Why will a dentist pull an abscess tooth that's still infected after antibiotics?

It is the cure: Antibiotics are hoped to relieve symptoms but are not a cure for and abscess tooth. Antibiotics can, but not always, reduce swelling. Reduced swelling makes treatment or extraction easier and allows local anesthetics to be more effective in blocking pain. Ultimately, the solution is the removal of the infection. The quickest way to accomplish this is an extraction with or without antibiotics.

Remove the source: The tooth is removed to get rid of the source of the infection. The antibiotics calm down the infection so the tooth can be extracted without complications.

Not a cure: Antibiotics cannot cure an abscess, only limit the spread of infection to reduce complications. "cure" requires root canal treatment and a cap or extraction, implant, and a cap. Infected tooth material must be physically removed...Antibiotics don't do that.

Still infected: The tooth needs further treatment, ie extraction or root canal. Antibiotics alone won't fix the problem.

Abscessed tooth: Some will and some won't. I can only speak for myself. In my opinion, if a tooth is abscessed and cannot be saved (or chosen not to), it should come out as soon as possible.The quicker it's out, the sooner the patient is comfortable and the sooner the healing process can begin. There are cases where antibiotic coverage is preferable or required (with certain medical conditions).